Story of Maths 4: To Infinity and Beyond

The Story of Maths episode 4 is about infinity and some of the mathematical problems introduced by Hilbert, as what the title of this episode says, “To infinity and Beyond”.

“Mathematics is about solving problems. Great unsolved problems make it alive”

David Hilbert, set 23 most important problems, mathematician should solve. His first problem emerged in East Germany. George Han Cantor studied infinity. He is the first person to understand the concept of infinity and gave it mathematical precision. According to him, there are many sizes of infinity such as infinity of fractions, infinity of whole numbers, etc. But there was one problem that he struggled to answer- continuum hypothesis.  “Is there an infinity between the smallest whole number and the largest infinity of the decimal numbers?”

In Paris, Henri Poincare was studying the orbit of the solar system. He answered whether the solar system continue turning like a clock or fly apart. When he finished doing his study, one of the editors found a problem. It was then called the Chaos theory

In Konigsberg, there are 7 bridges. People figured out how to pass the 7 bridges without crossing the bride twice.  Leonhard Euler gave his answer to this problem. According to him, it is not how each bridge is far from the other but how these bridges are connected with each other. This is what we call Topology. On the other hand, Poincare, studied topology as shapes evolved to something new or new way at looking at shape. But in 1994, Poincare had a problem; he couldn’t use topology in a 3-dimesional form such as the universe. This is called the Poincare conjecture.

Kurt Godel wanted to solve Hilbert’s second problem. He solved the Incompleteness Theorem. According to him, there are statements that are true but cannot be proved.

In America, Paul Cohen studied Cantor's continuum hypothesis. He consulted his work to Godel since his opinion was trusted by most people.  His method was new with a daring conclusion that no one understood; it was correct.

Julia Robinson solved Hilbert’s 10th problem, “are there universal method that could tell whether any equation had whole number solutions or not?” Robinson hypothesis was "no methods such existed. All you have to do is to take up one equation to a solution for the specific set of numbers" but he couldn’t find the set. Yuri Matiyasevich solved the 10th problem of Hilbert at the age of 22; and old Julia about it. Matiyasevich and Robinson worked together in solving other problems.

At the end of the Marcus du Sautoy’s journey, he went to his hometown to inspire the new generation about mathematics. He taught the Riemann hypothesis and imparted his knowledge of how this relate to the real world.

                I am amazed on how these mathematicians gave their dedication in analysing and solving problems, may it be in number or patterns in the real world. They live their lives solving math problems until they die. I can’t imagine it in my own life. Thinking about it seems I will lose my sanity. But the patience of analysing and their determination was the common characteristics of these mathematicians.

                I appreciate also what Du Sautoy did to his hometown. For me, gaining much knowledge is in vain if not shared; and Du Sautoy shared his knowledge to the new generation of his hometown. That’s the most important part of learning; is to teach what you’ve learned. I believe that wisdom is different from knowledge because wisdom is applying what you learned. Knowledge is just stored in your head. I hope to teach what I learned from the four episodes of this film The Story of Maths even though it is not that deep as what mathematicians explained their hypothesis or theory. But this film expanded my knowledge of mathematics and learned to appreciate it.